Copyright © 2009 Pearson Education, Inc. Chapter 9 Section 2 – Slide 1 AND

Copyright © 2009 Pearson Education, Inc. Chapter 9 Section 2 – Slide 1

AND

Chapter 9 Section 2 – Slide 2Copyright © 2009 Pearson Education, Inc.

Chapter 9

Geometry


WHAT YOU WILL LEARN

• Points, lines, planes, and angles• Polygons, similar figures, and

congruent figures• Perimeter and area• Pythagorean theorem• Circles• Volume


WHAT YOU WILL LEARN

• Transformational geometry, symmetry, and tessellations

• The Mobius Strip, Klein bottle, and maps

• Non-Euclidian geometry and fractal geometry


Section 2

Polygons


Polygons

Polygons are named according to their number of sides.

Icosagon20Heptagon7

Dodecagon12Hexagon6

Decagon10Pentagon5

Nonagon9Quadrilateral4

Octagon8Triangle3

NameNumber of Sides

NameNumber of Sides


Polygons (continued)

The sum of the measures of the interior angles of an n-sided polygon is (n 2)180.

Example: A certain brick paver is in the shape of a regular octagon. Determine the measure of an interior angle and the measure of one exterior angle.


Polygons (continued)

Determine the sum of the interior angles.

The measure of one interior angle is

The exterior angle is supplementary to the interior angle, so the measure of one exterior angle is180 135 = 45

( 2)180

(8 2)(180 )

6(180 )

1080

S n

1080135

8


Types of Triangles

Acute Triangle

All angles are acute.

Obtuse Triangle

One angle is obtuse.


Types of Triangles (continued)

Right Triangle

One angle is a right angle.

Isosceles Triangle

Two equal sides.

Two equal angles.


Types of Triangles (continued)

Equilateral Triangle

Three equal sides. Three equal angles, 60º each.

Scalene Triangle

No two sides are equal in length.


Similar Figures

Two polygons are similar if their corresponding angles have the same measure and the lengths of their corresponding sides are in proportion.

4

3

4

6

6 6

9

4.5


Example

Catherine Johnson wants to measure the height of a lighthouse. Catherine is 5 feet tall and determines that when her shadow is 12 feet long, the shadow of the lighthouse is 75 feet long. How tall is the lighthouse?

x

7512

5


Example (continued)

x

7512

5

Therefore, the lighthouse is 31.25 feet tall.

=

=

=

ht. lighthouse length of lighthouse's shadow=

ht. Catherine length of Catherine's shadow

x 75

5 1212 375

31.25

x

x


Congruent Figures

If corresponding sides of two similar figures are the same length, the figures are congruent.

Corresponding angles of congruent figures have the same measure.


Quadrilaterals

Quadrilaterals are four-sided polygons, the sum of whose interior angles is 360.

Quadrilaterals may be classified according to their characteristics.


Classifications

Trapezoid

Two sides are parallel.

Parallelogram

Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length.


Classifications (continued)

Rhombus

Both pairs of opposite sides are parallel. The four sides are equal in length.

Rectangle

Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. The angles are right angles.


Classifications (continued)

Square

Both pairs of opposite sides are parallel. The four sides are equal in length. The angles are right angles.

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Copyright © 2009 Pearson Education, Inc. Chapter 9 Section 2 – Slide 1 AND